From a completely water-filled cubical tank, 75 buckets of equal size are taken out, after which \(\frac{2}{5}\) of the tank remains filled with water. If each edge of the tank is 1.5 meters long, how much water does each bucket hold in liters?

Q. From a completely water-filled cubical tank, 75 buckets of equal size are taken out, after which \(\frac{2}{5}\) of the tank remains filled with water. If each edge of the tank is 1.5 meters long, how much water does each bucket hold in liters?

Let each bucket hold \(x\) liters of water. Since 75 buckets of water are removed, the tank becomes empty by \[ 1 - \frac{2}{5} = \frac{3}{5} \] Length of one edge of the cubical tank = 1.5 meters = 15 decimeters So, volume of the cubical tank \[ = 15^3 = 3375 \text{ cubic decimeters} \] Since 1 cubic decimeter = 1 liter, the tank holds a total of 3375 liters of water. According to the problem: \[ 75 \times x = 3375 \times \frac{3}{5} \Rightarrow x = \frac{3375 \times 3}{75 \times 5} = 27 \] Therefore, each bucket holds 27 liters of water.